Tree diameter distribution modelling: introducing the logit–logistic distribution

2005 ◽  
Vol 35 (6) ◽  
pp. 1305-1313 ◽  
Author(s):  
Mingliang Wang ◽  
Keith Rennolls
Keyword(s):  
Normal Distribution ◽  
Weibull Model ◽  
Diameter Distribution ◽  
Logistic Distribution ◽  
Parameter Distribution ◽  
Forest Modelling ◽  
Logit Transformation ◽  
Distribution Shape ◽  
Tree Diameter Distribution

Johnson's SB distribution is a four-parameter distribution that is transformed into a normal distribution by a logit transformation. By replacing the normal distribution of Johnson's SB with the logistic distribution, we obtain a new distributional model that approximates SB. It is analytically tractable, and we name it the "logit–logistic" (LL) distribution. A generalized four-parameter Weibull model and the Burr XII model are also introduced for comparison purposes. Using the distribution "shape plane" (with axes skew2 and kurtosis) we compare the "coverage" properties of the LL, the generalized Weibull, and the Burr XII with Johnson's SB, the beta, and the three-parameter Weibull, the main distributions used in forest modelling. The LL is found to have the largest range of shapes. An empirical case study of the distributional models is conducted on 107 sample plots of Chinese fir. The LL performs best among the four-parameter models.

scholarly journals A percentile-based estimator for the log-logistic function: Application to forestry

2020 ◽  
Vol 72 (1) ◽  
pp. 107-120
Author(s):  
Friday Nwabueze Ogana
Keyword(s):  
Estimation Method ◽  
Tectona Grandis ◽  
Logistic Function ◽  
Growth And Yield ◽  
Estimation Methods ◽  
Diameter Distribution ◽  
Logistic Distribution ◽  
Forest Stands ◽  
Forest Modelling ◽  
Diameter Distributions

AbstractDeveloping a simplified estimation method without compromising the performance of the distribution is germane to forest modelling. Few estimation methods exist for the Log-Logistic distribution and are relatively complex. A simplified estimator for the Log-Logistic parameters will increase its application in diameter distribution yield systems. Therefore, in this study, a percentile-based estimator was applied for the Log-Logistic distribution. The Kolmogorov-Smirnov, Anderson-Darling and Cramer-von Mises statistics were used to evaluate the method in two natural forest stands and two monospecific plantations of Gmelina arborea Roxb. and Tectona grandis Linn. f. in Nigeria. The parameter recovery model (PRM) and parameter prediction model (PPM) were used to predict the diameter distributions of independent stands of G. arborea and T. grandis. The results showed that the percentile estimator did not compromise the quality of fits of the Log-Logistic function across the four forest stands and are comparable to the maximum likelihood estimator. The 25th and 75th, and 40th and 80th were the best sample percentiles for the estimator. The predicted diameter distributions of G. arborea and T. grandis stands from the PRM and PPM were reasonable and compare well with the observed distribution. Thus, either of the models can be incorporated into the growth and yield system of forest stand management.

scholarly journals Thinning Response and Potential Basal Area in a Mixed Sub-humid Low-elevation Oak-Hornbeam Forest

2021 ◽  
Author(s):  
Mathias Neumann ◽  
Hubert Hasenauer
Keyword(s):  
Stand Structure ◽  
Basal Area ◽  
Climatic Conditions ◽  
Diameter Distribution ◽  
Stem Density ◽  
Growing Stock ◽  
A Site ◽  
Water Nutrients ◽  
Related Mortality

Abstract Competition for resources (light, water, nutrients, etc.) limits the size and abundance of alive trees a site can support. This carrying capacity determines the potential carbon sequestration in alive trees as well as the maximum growing stock. Lower stocking through thinning can change growth and mortality. We were interested in the relations between stand structure, increment and mortality using a long-unmanaged oak-hornbeam forest near Vienna, Austria, as case study. We expected lower increment for heavy thinned compared to unmanaged stands. We tested the thinning response using three permanent growth plots, whereas two were thinned (50% and 70% basal area removed) and one remained unmanaged. We calculated stand structure (basal area, stem density, diameter distribution) and increment and mortality of single trees. The heavy thinned stand had over ten years similar increment as the moderate thinned and unthinned stands. Basal area of the unthinned stand remained constant and stem density decreased due to competition-related mortality. The studied oak-hornbeam stands responded well even to late and heavy thinning suggesting a broad “plateau” of stocking and increment for these forest types. Lower stem density for thinned stands lead to much larger tree increment of single trees, compared to the unthinned reference. The findings of this study need verification for other soil and climatic conditions.

Estimation and calibration of stem diameter distribution using UAV laser scanning data: A case study for larch (Larix olgensis) forests in Northeast China

2022 ◽  
Vol 268 ◽  
pp. 112769
Author(s):  
Yuanshuo Hao ◽  
Faris Rafi Almay Widagdo ◽  
Xin Liu ◽  
Ying Quan ◽  
Zhaogang Liu ◽  
...  
Keyword(s):  
Northeast China ◽  
Laser Scanning ◽  
Stem Diameter ◽  
Diameter Distribution ◽  
Larix Olgensis

scholarly journals Modeling Diameter Distribution of Black Alder (Alnus glutinosa (L.) Gaertn.) Stands in Poland

Forests ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 412 ◽  
Author(s):  
Piotr Pogoda ◽  
Wojciech Ochał ◽  
Stanisław Orzeł
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Alnus Glutinosa ◽  
Weibull Model ◽  
Diameter Distribution ◽  
Stand Age ◽  
Weibull Function ◽  
Black Alder ◽  
Kolmogorov Smirnov ◽  
Non Parametric

We present diameter distribution models for black alder (Alnus glutinosa (L.) Gaertn.) derived from diameter measurements made at breast height in 844 circular sample plots set in 163 managed stands located in south-eastern Poland. A total of 22,530 trees were measured. Stand age ranged from six to 89 years. The model formulation was based on the two-parameter Weibull function and a non-parametric percentile-based method. Weibull function parameters were recovered from the first raw and second central moments estimated using the stand quadratic mean diameter. The same stand characteristic was used to predict values of 12 percentiles in the percentile-based method. The model performance was assessed using the k-fold cross-validation method. The goodness-of-fit statistics include the Kolmogorov–Smirnov statistic, mean error, root mean squared error, and two variants of the error index introduced by Reynolds. The percentile model developed, accurately predicted diameter distributions in 88.4% of black alder stands, as compared to 81.9% for the Weibull model (Kolmogorov–Smirnov test). Alternative statistical metrics assessing goodness-of-fit to empirical distributions suggested that the non-parametric percentile model was superior to the parametric Weibull model, especially in stands older than 20 years. In younger stands, the two models were accurate only in 57% of the cases, and did not differ significantly with respect to goodness-of-fit measures.

scholarly journals Probability Distributions for a Quantile Mapping Technique for a Bias Correction of Precipitation Data: A Case Study to Precipitation Data Under Climate Change

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1475 ◽  
Author(s):  
Jun-Haeng Heo ◽  
Hyunjun Ahn ◽  
Ju-Young Shin ◽  
Thomas Rodding Kjeldsen ◽  
Changsam Jeong
Keyword(s):  
Climate Change ◽  
Bias Correction ◽  
Shape Parameter ◽  
Mapping Method ◽  
Distribution Model ◽  
Parameter Distribution ◽  
Precipitation Data ◽  
Distribution Models ◽  
Quantile Mapping

The quantile mapping method is a bias correction method that leads to a good performance in terms of precipitation. Selecting an appropriate probability distribution model is essential for the successful implementation of quantile mapping. Probability distribution models with two shape parameters have proved that they are fit for precipitation modeling because of their flexibility. Hence, the application of a two-shape parameter distribution will improve the performance of the quantile mapping method in the bias correction of precipitation data. In this study, the applicability and appropriateness of two-shape parameter distribution models are examined in quantile mapping, for a bias correction of simulated precipitation data from a climate model under a climate change scenario. Additionally, the impacts of distribution selection on the frequency analysis of future extreme precipitation from climate are investigated. Generalized Lindley, Burr XII, and Kappa distributions are used, and their fits and appropriateness are compared to those of conventional distributions in a case study. Applications of two-shape parameter distributions do lead to better performances in reproducing the statistical characteristics of observed precipitation, compared to those of conventional distributions. The Kappa distribution is considered the best distribution model, as it can reproduce reliable spatial dependences of the quantile corresponding to a 100-year return period, unlike the gamma distribution.

Design Method for Lattice-Skin Structure Fabricated by Additive Manufacturing

2014 ◽  
Author(s):  
Yunlong Tang ◽  
Yaoyao Fiona Zhao
Keyword(s):  
Complex Geometry ◽  
Lattice Structure ◽  
Design Method ◽  
Mapping Function ◽  
Second Step ◽  
Parameter Distribution ◽  
Skin Structure ◽  
Traditional Design ◽  
Novel Design

Parts with complex geometry structure can be produced by AM without significant increase of fabrication time and cost. One application of AM technology is to fabricate customized lattice-skin structure which can enhance performance of products with less material and less weight. However, most of traditional design methods only focus on design at macro-level with solid structure. Thus, a design method which can generate customized lattice-skin structure for performance improvement and functionality integration is urgently needed. In this paper, a novel design method for lattice-skin structure is proposed. In this design method, FSs and FVs are firstly generated according to FRs. Then, initial design space is created by filling FVs and FSs with selected lattice topology and skin, respectively. In parallel to the second step, initial parameters of lattice-skin structure are calculated based on FRs. Finally, TO method is used to optimize parameter distribution of lattice structure with the help of mapping function between TO’s result and lattice parameters. The design method proposed in this paper is proven to be efficient with case study and provides an important foundation for wide adoption of AM technologies in industry.

Research on Influence of Wetting Fluid by Gas Bubble Method to Measure Pore Size Characteristics

2014 ◽  
Vol 1048 ◽  
pp. 498-502
Author(s):  
Peng Zhang ◽  
Bing Xuan Ni
Keyword(s):  
Normal Distribution ◽  
Pore Diameter ◽  
Diameter Distribution ◽  
Gas Bubble ◽  
Distribution Characteristics ◽  
Measurement Results ◽  
Dimethyl Silicone ◽  
Composite Nonwoven ◽  
Liquid Measurement ◽  
Wetting Liquid

In this paper, the experimental of pore diameter distribution characteristics of spunbond and meltblown composite nonwoven is carried out by using of gas bubble method. The influence of 7 kinds of wetting liquid to measurement results is studied, including of Galwick, Porefil, Silpore, Silwick, Dimethyl silicone, Isopropanol and Alcohol. The results show that wetting liquids of Galwick, Silwick and Dimethyl silicone can obtain the consistent value of pore diameter, meanwhile, have nearly normal distribution characteristics of pore diameter. Therefore, the wetting liquids of Galwick, Silwick and Dimethyl silicone are ideal wetting liquid for nonwoven. While the other four kinds of wetting liquid measurement results vary greatly, and don’t show normal distribution, they are not suitable as the wetting liquid of nonwoven by gas bubble method.

Intelligent Compaction for Quality Control and Acceptance for Soil and Base Compaction through Statistical Analysis

2018 ◽  
Vol 2672 (52) ◽  
pp. 325-332
Author(s):  
Jimmy Z. Si
Keyword(s):  
Quality Control ◽  
Normal Distribution ◽  
Data Distribution ◽  
Statistical Methodology ◽  
Mapping Data ◽  
Intelligent Compaction ◽  
Subgrade Soil ◽  
Field Compaction ◽  
Aggregate Base

This paper presents the results of the intelligent compaction data that were collected from various layers including subgrade soil, lime-treated subgrade, cement-treated base and flexible aggregate base layers. Sets of proof-mapping data were collected from each layer upon completion of compaction. The data was then downloaded and analyzed using a computer program. Based on the data analysis and field compaction observation, a new statistical methodology for analyzing intelligent compaction data is proposed. The method is used to assess the uniformity of soil and base compaction quality and this is successfully demonstrated through a case study. A typical normal distribution of an intelligent compaction dataset indicates that a good and uniform compaction is achieved. It is, therefore, possible to assess the compaction quality by evaluating the perfection of normal districtuion of an intelligent compaction (IC) dataset. The compaction uniformity is evaluated by a compaction uniformity index, which is defined as the ratio of the probability within the specified limits in a field compaction data distribution to the probability in a target normal distribution.

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